RETOS. Nuevas Tendencias en Educación Física, Deporte y Recreación ISSN: 1579-1726 [email protected] Federación Española de Docentes de Educación Física España

Calero Morales, ; Fernández Lorenzo, Angie; García López, Pedro Antonio; Chávez Cevallos, Enrique Anomalies in effectiveness: A mathematical model used in international RETOS. Nuevas Tendencias en Educación Física, Deporte y Recreación, núm. 32, julio- diciembre, 2017, pp. 194-198 Federación Española de Docentes de Educación Física Murcia, España

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Anomalías de la efectividad: un modelo matemático utilizado en el voleibol internacional Anomalies in effectiveness: A mathematical model used in international volleyball *Santiago Calero Morales, *Angie Fernández Lorenzo, **Pedro Antonio García López, * Enrique Chávez Cevallos *Universidad de las Fuerzas Armadas ESPE (Ecuador), **Universidad Técnica de Machala (Ecuador)

Abstract. Based on the analysis of the mathematical statistical model «Effectiveness», internationally used to process technical-tactical performance in Volleyball, and also to determine its target under the concept «Effectiveness», including its basic characteristics, the paper demonstrates the existence of three mathematical anomalies in the formula. These anomalies are described through examples, including a population-based study that determined that the technical-tactical action Service, Dig and Block have more negative than positive actions, closely related to a fundamental anomaly that causes inaccurate interpretations of reality. Key words: Effectiveness Model, Volleyball, Technical Tactical Performance, Anomaly

Resumen. Partiendo del análisis del modelo matemático de «Efectividad», utilizado internacionalmente para procesar el rendimiento técnico-táctico del Voleibol, y luego de determinar su objetivo atendiendo al concepto «Efectividad», así como sus características básicas, en el artículo se demuestra la existencia de tres anomalías en la fórmula. Dichas anomalías son expuestas a través de ejemplos, donde se incluye un estudio poblacional que determina que los fundamentos técnico-tácticos Saque, Defensa de Campo y Bloqueo presentan más acciones negativas que positivas, aspecto estrechamente relacionado con una anomalía fundamental que provoca interpretaciones inexactas de la realidad. Palabras clave: Modelo Efectividad, Voleibol, Rendimiento Técnico-Táctico, Anomalía

Introduction the real quality of the variable. For that reason, since there are several variables that have significant influence in the performance (according A model is considered as an abstract representation of some aspects to the technical-tactical actions studied), ones would positively impact of reality (Gallagher & Watson 2005; Encarta 2009; González & Guillén, in scoring and others would have a negative impact, and also each 2013; Thalheim, 2013). The modelling in sport is usually employed, variable will diverge form the other according to the existing significant commonly manifested in the design of exercises that simulate reality differences in relation to the final performance (Calero, 2009-2011). game, exercises that make theoretical and practical situations that have Some mathematic models obtain an approximate description of the happened in the competition, as is the case of technico-tactical complexes phenomenon and in that case it is necessary to check precision if the or K-1 and K-2 (Fiedler et al 1974; Morales & Taboada, 2012; Suárez, results are not satisfactory the model should be formulated again using Rabaz, Fernández, Gil, & Arroyo, 2017), the typical phases (Fröhner mathematic language (Tang, 2005; Tanner y Gore, 2013; Hatano, Hirata, 2004, Martinez 2012) or the simplified situation of the Game (Andux, Suzuki y Aihara, 2015). 2012). In Mesquita, Marques & Maia (2001); Salas, Palou & Schelling However, the models through exercise are not the only used in the (2004); Oliveira, Mesquita & Oliveira (2005); Calero (2007-2009); Gil, process of management of sports training. The statistics by making Del Villar, Moreno, García & Moreno, (2011); FIVB, (2003-2005), the physical representations of symbols, simply summarizes phenomena data of the technical-tactical performance of several techniques and and equations, concepts and theories for studying complex systems training categories have been tabulated, recording different actions that (Tormos & Lova, 2003; Gallagher & Watson, 2005; Hong, 2013). are usually modelled with Effectiveness and although each paper has its Therefore, mathematical models are formed by elements that characterize own objective, there are common patterns that undoubtedly typify a one or more aspects of the reality modelled (Aracil 1983), in order to technical-tactical action, as the prevalence of negative actions over the extract properties and characteristics of the relationships among the positive ones in techniques such as Block, Serve and Dig. elements, which otherwise would remain hidden and illogical. Effectiveness is, according to its definition, «the ability to reach the In the specific case of statistical models to estimate the charge of effect wanted or desired» (RAE, 2015). Effectiveness as a concept is technical and tactical performance of volleyball, these actions make the equivalent to reality, certainty, security, validity, warranty (Compact technical and tactical variables that evaluate (according to an objective Ocean 2006; Cervantes 2008, Encarta 2009), thus, the primary objective and a specific function), the technical and tactical performance of the model «Effectiveness» is to determine the level of security that individually and collectively in order to obtain information related to the has a player or computer when executing technical-tactical actions in process of attracting talent, the exploration of opposites, the evaluation the game, this means that if a player gets more points than what he of competitive performance, and delivering specialized information to loses, a player is safe, accurate, effective, otherwise it will be a player media, researchers, managers, among others (Coleman, 2002; Velasco insecure, not certain, ineffective1. Therefore, the variables that represent quoted by Alonso, 2003; Hohmann, Lames & Letzeier, 2005; Poyato, that concept should symbolize this reality from the mathematical point 2007; Calero, 2009; Silva, Domínguez, Echeverría, Rabaz, & Arroyo, of view, hence their assessment is in line with that quality. 2016). Therefore, applied statistics is considered as one of the most Effectiveness as a mathematic model uses three significantly important aspects for a coach (Coleman, 2002; Thiess, Tschiene & influential variables in the final performance (Calero, 2009-2010), it is Níkel, 2005; Clarke & Skiba, 2013), both in competitions and in training. internationally used by different authors and softwares specialized in The construction of a mathematical model requires the full applied statistics. In StatTrak for Volleyball, v6.01 (1998); VBSTATS32 employment of concepts, since they classify reality, recalling the V3.2.0E (2002); FIVB (2003-2005); VolleySoft MultiPasport (2005); objective of the model as a mean to aid in the analysis and understanding Mesquita, Marques & Maia (2001); Sydex Volleyball Stats, (2002); of the reality to be measured (Dror, 1986; Tormos & Lova, 2003; Oliveira, Mesquita & Oliveira (2005); League Analyzer for Volleyball Arsham, 2015). v3.2.0 (2005); Volleyball Statware v6, (2006) and Quality Stats Volleyball According to the concept, each processed variable is given a numeric V10.1.0, (2010)2 is shown a wide use of that mathematic formula. value, making up the design of the formula, a value that must represent The content analysis of the model anticipates statistic anomalies, understanding by anomaly the discrepancy of the model in regard to certain rule or use, in other words, an irregularity. These rules are Fecha recepción: 22-04-16. Fecha de aceptación: 14-02-17 enumerated in the material and methods epigraph described in Calero Santiago Calero Morales [email protected] (2009); an aspect that causes alterations in the estimation of the technical-

- 194 - Retos, número 32, 2017 (2º semestre) tactical performance and therefore in the eventual decision-making. The variables registered (for all the examples will be used the Block For that reason, the central objective of the paper consists on actions, except for Tables 4 & 5) are represented by the following demonstrating which are those irregularities or anomalies, and how they methodology: impact negatively on the process of technical-tactical control of Volleyball, - Positive values (Ap): The Block gets the point a key factor in the process of sports training management. - Negative values (An): The block commits a technical foul penalized by the referee, or the lock throws the ball beyond the reach of other Material and Methods players. - Slash actions (AS): They belong to the rest of the variables that This concept is conceptualized through the formula or statistical make up the above categories. Example: The ball bounces behind the model, available in the following structure: lock, obtain or not the offensive initiative. For that matter, this variable Model «Effectiveness» is creating opportunities for the opponent. − A≠0 (Ap An) Results = T (n) *100 Ef Ν The statistical model «Effectiveness» presents three anomalies ( j;e;c) that alter the outcome. These are: t t Where i is the player and t the technique selected AP i and AN i the 1. Their results show negative rating scale number of positive and negative technical-tactical actions in the technique 2. The equivalence between the variables the numerator, creates t of the player i, respectively, and Nt the total of actions in the technique zero values, not representative of performance in terms of individual t of the player i. Likewise, the total effectiveness of a team or a tournament comparison. is defined as the sum of each of the individual effectiveness of every 3. When generating a negative scale, the result is not congruent player in the team or the tournament. Anomaly Number One, «the negative scales» (shown in the example In order to show the above mentioned anomalies, some real scoring of Table 1), with locking action made by a player in the first game, groups have been analyzed. The first one the Block performance of the provides a result of -13,33%. This way of presenting quantitative RSA3 player in three games of the qualifiers of the IV National Volleyball information tends to have drawbacks, for it provides a negative datum, League (Table 1), obtained by the Effectiveness model. an aspect that infers decreases and contributes to the third and more However, to know the level of incidence equal to or less than zero, important anomaly. obtained by mathematical calculation in the numerator of the formula Table 1: were analyzed the scores of two national high level championships, in Analysis of three results obtained with the model "Effectiveness" in three different games. both genders (Tables 4 and 5). For both cases, was processed the ACTION GAME 1 GAME 2 GAME 3 population of executed actions (9413 in males and 8 683 in females) in AP 2 2 AN 2 2 2 the finals of the National Volleyball League IV. 2007, recording AS 13 15 17 14 games of 14 possible, held on 08.03.2007 to 15.03.2007. TOTAL 15 19 21 Calculation: -13.33% 0% 0% Content Analysis as theoretical methods, values the model «Effectiveness» in accordance with five rules formed to evaluate the Table 2: process of technico-tactical performance, set by (Calero 2009). Analysis of four results with the model "Effectiveness" in four different games. Congruent values There are: KIND OF ACTIONS GAME 1 GAME 2 GAME 3 GAME 4 AP 32 32 32 32 1. You must determine the proposed function and objective. AN 25 25 25 25 2. You should include all variables that influence positively depending AS 20 21 40 150 TOTAL777897207 on its function and objective. Calculations: 9.09% 8.97% 7.22% 3.38% 3. You should have a correct mathematical modelation relating to its function and objective. In game number two and three in the table above, you can represent 4. The measure unity should be the most adequate to the social the second anomaly Mathematics, «The equivalence between the va- enviroment it is applied. riables in the numerator. Here, although the player is regular4, the for- 5. The numeric value assigned to each variable must correspond to mula shows a figure that would be zero for games two and three. The real quality. problem occurs when the amount of opposite variables of the numerator

Therefore, indicators of contending analysis are in correspondence are equal (AP y AN). with those rules, emphasizing, for this study case, rules One and Three. The Third Mathematic Anomaly «Non-congruent values» are To register and process the volleyball actions was used the represented in Table 2, using a hypothetical example for better ControlVolei Competencia v1 software, and to tabulate the data understanding. Microsoft Excel 2010. After performing the calculation in the numerator (for all cases equals seven games), and having processed values at each step, the Study Variables model obtains results that match the athletic performance. In all cases The statistical model «Effectiveness» uses three variables the result expressed numerically decreases progressively. significantly influencing the technico- tactical performance of volleyball. It corresponds to the real value of a player that will generate the These are: above actions, which is determined based on the concept that the more 1. The values of evaluative maximum performance range (positive, opportunities you provide to the contrary in its mid-game, the greater Ap) the chance of successful adversary, therefore, the effectiveness decreases 2. The values of evaluative lower-ranking performance (Negative; with increasing the opportunities of the opponent. In every game, the An) volleyball player gives more opportunities to the rival (20, 21, 40 and 3. All other values different from previous issues (causing no losses 150, respectively; Actions Slash: As) under the same value of the of these points in absolute terms, AS) joined to all the categories of numerator (7), therefore the result will decrease in each game ( 9.09%, registered actions. 8.97%, 7.22%, 3.38%, respectively). This behavior is seen as consistent The first two values can be seen in the numerator, which are or logical, since the model acts positively as expected; prompting him in computed by a subtraction, or are antagonistic, mathematically creating every game there is a decrease in effectiveness, as it is shown in graphic two variables. The third variable is represented by the sum of all the I. actions or variables registered in the denominator.

Retos, número 32, 2017 (2º semestre) - 195 - In Table 4, the negative values obtained with the calculation of the VALUES OBTAINED FROM THE EFFECTIVENESS MODEL numerator are common to the technical-tactical actions Serve, Dig and

10 Block, and non-existent for the rest of the techniques, an aspect that is 1; 9,09 2; 8,97 8 3; 7,22 6 described in details in Graphic 3. 4 4; 3,38 2 Table 5: 0 1234 Acquisition of mathematical values of the numerator less than or equal to zero (CN = 0). Final Phase of the IV National Volleyball League . Gender Female. Graphic 1: Values obtained consistent with the calculation of the effectiveness model. SPIKE BLOCK SERVE Table 3: AP AN AS TOTAL CN AP AN AS TOTAL CN AP AN AS TOTAL CN Analysis of four results with the model "Effectiveness" in four different games. 38611553220183068211546626 Incongruent values 62 12 13 87 50 11 10 26 47 1 6 8 69 83 -2 KIND OF ACTIONS GAME 1 GAME 2 GAME 3 GAME 4 81 11 46 138 70 11 13 21 45 -2 3 6 52 61 -3 AP 25 25 25 25 3 9 16 58 24 9 12 22 43 -3 7 10 52 69 -3 AN 32 32 32 32 67 21 37 125 46 8 13 26 47 -5 8 11 79 98 -3 AS 20 21 40 150 33 11 17 61 22 9 16 14 39 -7 3 6 94 103 -3 TOTAL777897207 49 16 37 102 33 9 17 18 44 -8 14 18 48 80 -4 Calculations: -9.09% -8.97% -7.22% -3.38% 66 27 35 128 39 12 24 18 54 -12 1 5 64 70 -4 53 22 38 113 31 10 22 45 77 -12 12 16 90 118 -4 67 35 32 134 32 6 19 13 38 -13 11 16 51 78 -5 Table 3 uses the same numeric values that Table 2, although the 51 24 41 116 27 6 24 17 47 -18 23 29 65 117 -6 48 28 18 94 20 12 31 15 58 -19 6 14 58 78 -8 values of the Effectiveness model numerator (AP and AN) have been 21 9 27 57 12 4 25 11 40 -21 3 12 72 87 -9 inverted to favour understanding, obtaining in all cases the value of -7 43 23 45 111 20 9 30 37 76 -21 6 16 35 57 -10 43 28 51 122 15 12 33 38 83 -21 7 17 49 73 -10 (25-32 = -7). By completing the calculations in the formula the values 43 33 45 121 10 13 44 26 83 -31 9 20 89 118 -11 25 60 66 151 -35 10 25 77 112 -15 obtained with the model grow as opportunities increase the contrary 9563499-479284178-19 (20, 21, 40 and 150; Calculation: -9.09% -8.97% -7.22%; -3.38% RECEIVER DIG SET AP AN AS TOTAL CN AP AN AS TOTAL CN AP AN AS TOTAL CN respectively). This phenomenon is established where the value of the 93 6 44 143 87 6 10 10 26 -4 70 13 452 535 57 numerator is in the negative scales, since under this condition, the larger 75 11 26 112 64 9 13 11 33 -4 42 6 403 451 36 72 10 37 119 62 7 12 8 27 -5 42 6 438 486 36 the divisor, will approach zero over the result, and therefore the smaller 58 8 30 96 50 9 14 11 34 -5 33 10 457 500 23 85 10 56 151 75 7 14 11 32 -7 the numerical value of a negative scale, the higher their mathematical 78 14 39 131 64 11 19 14 44 -8 value. Graphic 2 represents graphically the above. 59 7 41 107 52 7151739-8 91 21 40 152 70 25 34 23 82 -9 81 13 54 148 68 6 16 10 32 -10 30 5 25 60 25 7 18 8 33 -11 VALUES OBTAINED FROM THE 2142146176171437-11 EFFECTIVENESS MODEL 57 15 43 115 42 8202149-12 0,00% 30732692312242056-12 1234 -2,00% 58 19 41 118 39 15 29 20 64 -14 51 23 40 114 28 8231041-15 -4,00% 4; -3,38% 4201943-16 -6,00% 11 30 14 55 -19 3; -7,22% -8,00% 1; -9,09% 2; -8,97% -10,00% As in table 4 referring to the male gender, Table 5 shows that in the Graphic 2: Non-consistent values obtained with the calculation of the effective model. case of female gender, the technical-tactical actions Serve, Defense and Block present a high coincidence of negative values inside the numerator’s Table 4: calculation. Derivation of mathematical values of numerators less than or equal to zero (CN = 0). Final Phase of the IV National Volleyball League. Gender Male. SPIKE BLOCK SERVE AP AN AS TOTAL CN AP AN AS TOTAL CN AP AN AS TOTAL CN Percentage of technical-tactical actions 438308135149184159 3921046 that have a CN=0 68 25 34 127 43 15 13 15 43 2 9 5 87 101 4 100,00 Dig; 95,24 Block; 85,71 80 24 73 177 56 14 13 42 69 1 13 9 80 102 4 90,00 Service; 80,00 47 19 27 93 28 10 12 18 40 -2 9 6 104 119 3 80,00 37 14 28 79 23 26 29 48 103 -3 3 3 51 57 0 70,00 60,00 27926621810141943-4137276-2 50,00 6 24 58 147 41 10 15 37 62 -5 6 8 75 89 -2 40,00 72 33 43 148 39 10 16 17 43 -6 3 6 54 63 -3 30,00 62 24 60 146 38 6 15 30 51 -9 3 6 55 64 -3 20,00 75 34 53 162 41 11 21 16 48 -10 2 7 50 59 -5 10,00 Spike; 0,00Receiver; 0,00 Set; 0,00 0,00 40 1 30 88 22 26 36 49 111 -10 5 10 77 92 -5 123 71 4 66 171 37 15 26 40 81 -11 12 18 55 85 -6 Technical-tactical actions. Man 66 37 45 148 29 7 19 14 40 -12 9 15 64 88 -6 30 17 38 85 13 6 18 22 46 -12 2 9 49 60 -7 20 17 22 59 3 12 24 30 66 -12 8 15 65 88 -7 Percentage of technical-tactical actions 8 22 17 47 -14 19 26 82 127 -7 that have a CN=0 7222150-158165579-8 120,00 27 42 69 138 -15 6 14 87 107 -8 Service; 94,44 Dig; 100 14 31 35 80 -17 5 19 61 85 -14 100,00 Block; 88,89 6251849-195203964-15 80,00 4243159-20 60,00 RECEIVER DIG SET 40,00 AP AN AS TOTAL CN AP AN AS TOTAL CN AP AN AS TOTAL CN 20,00 57 6 34 97 51 26 25 22 73 1 149 4 348 501 145 Spike; 0,00Receiver; 0,00 Set; 0,00 103 14 54 171 89 9 13 11 33 -4 122 3 395 520 119 0,00 123 95 13 53 161 82 10 14 15 39 -4 59 6 428 493 53 Technical-tactical actions. Women 113 9 84 206 104 12 17 15 44 -5 39 10 337 386 29 37524663213201952-7 54 5 44 103 49 2 12 16 30 -10 Graphic 3: For hundreds of calculations obtained from the numerator less than or equal to zero 49 7 46 102 42 8 20 24 52 -12 CN = 0 for each technical-tactical action of volleyball. both genders. 55853116477202552-13 63 13 57 133 50 2 16 13 31 -14 Graphic 3 show the percent incidence of values less and equal to 63 14 56 133 49 4 19 9 32 -15 30 8 22 60 22 6 22 21 49 -16 zero, obtained after the calculation of the numerator: CN d»0, for both 47 13 41 101 34 3 20 14 37 -17 genders. That shows that the values have a high percent incidence in the 26 6 34 66 20 4 23 13 40 -19 56 20 66 142 36 6 27 16 49 -21 Block, Serve and Dig action (Block: 85.71% and 88.89%; Serve: 80.00% 20 13 28 61 7 3 24 33 60 -21 18 40 11 69 -22 and 94.44%; Dig: 95.24% and 100%, male and female respectively), 23 12 35 -23 while such value are not presented in the technical-tactical actions Spike, 1251339-24 11 35 21 67 -24 Receive and Set, respectively (Spike: 0.00%; Receive: 0.00%; Set: 0.00%, 3281344-25 male and female5), according to the individual evaluation of all the 9432476-34 regular players that participate in the Finals of the Fourth National

- 196 - Retos, número 32, 2017 (2º semestre) Volleyball League. The aforementioned shows that the result in the analyzed, as the one made in Block by Oliveira et als. (2005), distort the numerator (CN < 0) is common in high performance volleyball. result expected and therefore the data is wrongly interpreted, taking into account that the more the technical-tactical opportunities given to Discussion the rival, the more probabilities of losing a point, and therefore the final value should decrease in the final Effectiveness equation. Since the Effectiveness statistic model is internationally and However, Effectiveness under the condition CN < 0 raises the final functional in several research papers and softwares of applied statistics value as the AS actions increase, or increases the value as the technical- to Volleyball such as StatTrak for Volleyball, v6.01 (1998); Mesquita et tactical opportunities given to the rival increase. This contradiction als, (2001); Sydex Volleyball Stats (2002); VBSTATS32 V3.2.0E, (2002); causes uncertainty in the estimation of the technical-tactical performan- FIVB, (2003-2005); VolleySoft MultiPasport (2005); Oliveira et als., ce, coinciding with the affirmation made by Tang (2005) that models (2005); League Analyzer for Volleyball v3.2.0 (2005); Volleyball Statware with similar imprecision should be reformulated. Therefore, if the v6, (2006) y Quality Stats Volleyball V10.1.0, (2010), among others, Effectiveness model is used, the rankings of the Block, Serve and Dig the reliability of the mathematic instrument should positively respond actions will distort reality, since ever AS action will wrongly increase under any condition. the numeric performance of a player, when if should reduce it. However, when the result of the numerator equals zero, the numerical The Effectiveness statistic model as it generates equal or lesser values processed, regardless of the amount and importance, cause equal values than zero after the calculation of the numerator (Anomaly 1 and results (Table 1: game 2 and 3: 0 percent respectively). Another real 2), creates inconsistent values (Anomaly 3). The three anomalies example is available in Table 4: in the Serve action, whichis colored in previously noted do not fulfil the third rule for processing the technical- blue, and in the ranking best block, best serve and best dig of the World tactical performance; since it has a wrong mathematical modelling in Championship 2011(FIVB, 2011a,b,c), which demonstrates that it relation with the objective pursued (determine effectiveness). That happens regularly. implies that the model does not determines correctly the goal of the In Calero (2009) was studied the Finals of the Volleyball World authors (Rule number 1) when the CN < 0 condition is present, having League held in , , and it was defined that the probability a negative influence in the estimation of the individual and collective to lose one point after an AS action in Block is 47,78 percent, and the performance of the technical-tactical actions of volleyball, with emphasis probability to score a point 25,06 percent (Difference: 22,72 percentage in Serve, Dig and Block. points more in favour of losing a point); for which the AS Blocking That allows affirming that the Effectiveness statistic model, after actions give the opponent more advantages. Therefore, the AS action calculating the numerator and presenting the condition CN < 0, shows should be statistically interpreted as a variable that reduces the final a false fulfilment of the goal, causing three mathematic anomalies that value obtained by the Effectiveness model. The Table 1 predicts imply false interpretations of the reality. estimation errors of the technical-tactical performance of the Block, concerning the RSA player, who in games 2 and 3 has the same result (0 Conclusions percent) even performing different actions AS (15 and 17 respectively) under the same numerator value. That indicates that the model equals The above can generally conclude that: Effectiveness in the statistical performance when actually had substantial variations in the actions. model is identified under the condition CN < 0, obtained in the processing Each significantly influential action will have more or less probabilities of the variables in the numerator of the formula referenced, three of losing or winning a point, as it is the case of the setter demonstrated anomalies that adversely affect the performance estimation of technical- in Calero (2009, 2011), and the rest of the technical-tactical action. tactical Volleyball, causing certain false conditions and interpretations Therefore, as there are differences in then Slash (AS) actions, there must of the final performance. For that reason, the use of the Effectiveness be numerical differences in the final result of the equation. statistical model should be applied on those technical-tactical actions This player, if compared to one that has never played, seemed to with more positive actions than negative ones (Spike, Receive and Set), have the same numeric value (0). Then, reality affirms that not playing while its application must be excluded from those fundamentals that equals doing nothing in practice, and having two positive actions (AP), regularly obtain more negative actions than positive ones (Block, Dig, two negative (AN) and 15 Slash (AS) (Table 1) equals influential values Serve). in higher or lesser numbers for the technical-tactical performance. That causes two problems for the coach, the first situation would be the Autor Notes impossibility of comparing a regular player and a bench one (both would have a numeric value of zero); the second situation will be related 1. In the paper the word Ineffective is considered an antonym of to the competitive ranking, since an A player with a numeric value of 0 Effective. will mathematically overcome every player with more negative than 2. Not all authors have the same organization for the previously positive actions, although the A player as an excessively higher amount described model, although the structure is similar. of Slash (SA) actions; therefore, the coach will make a mistaken analysis 3. By ethical reasons, the name of the player is omitted. of the individual performances, which would cause taking wrong 4. A regular player is that who plays and participates in several decisions. actions of the game, meaning that the team depends on his performance. The previous anomaly derives from the possibility that the 5. Although in the competitions analyzed the regular players had technical-tactical variables have equal negative and positive actions, no negative values higher than the positive ones (CNd»0), in the case of since the Effectiveness model is able to generate negative values (anomaly Spike, Receive and Set, other national competitions have had them, 1). especially in younger categories, according to studies made in other The error of the Effectiveness model negatively increases the competitions available in Calero (2007-2009). estimation of the technical-tactical performance by presenting more negative actions than positive ones (Serve, Dig, Block), an common Acknowledgments aspect demonstrated in tables 4 and 5 and represented in graphic 3. That characteristic in the action of the technical-tactical actions previously To the Programa Prometeo de la Secretaría Nacional de Educación described have been widely corroborated by other sources, such as Superior, Ciencia, Tecnología e Innovación de la República del Ecuador Mesquita, Marques & Maia (2001); Salas, Palou & Schelling (2004); Oliveira, Mesquita & Oliveira (2005); Calero, (2009); Gil et als (2011); References FIVB (2003, 2011a,b,c), an inconvenient increased in younger categories (Calero, 2007), for which the research carried out from the model Ace Volleyball Analyzer v7. (2009). Dimensional Software Inc. USA

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